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A ball travels on a parabolic path in which the height (in feet) is given by the expression $$-25t^2+75t+24$$, where t is the time after launch. At what time is the height of the ball at its maximum?

Oct 21, 2019

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+9129
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A ball travels on a parabolic path in which the height (in feet) is given by the expression $$-25t^2+75t+24$$, where t is the time after launch. At what time is the height of the ball at its maximum?

Ein Ball bewegt sich auf einem parabolischen Pfad, bei dem die Höhe (in Fuß) durch den Ausdruck gegeben ist, wobei t die Zeit nach dem Start ist. Wann ist die Höhe des Balls am größten?

$$\color{BrickRed}h(t)=-25t^2+75t+24\\ \frac{dh}{dt}=-50t+75=0\\ \color{blue}t=1.5$$

$$h=-25\cdot 1.5^2+75\cdot1.5+24\\ \color{blue}h=80.25$$

The ball reaches its maximum height of 80.25 feet after 1.5 time units.

!

Oct 21, 2019
edited by asinus  Oct 21, 2019

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this is actually just asking for the bigger root of the quadratic!

Oct 21, 2019
#2
+9129
+2

A ball travels on a parabolic path in which the height (in feet) is given by the expression $$-25t^2+75t+24$$, where t is the time after launch. At what time is the height of the ball at its maximum?

Ein Ball bewegt sich auf einem parabolischen Pfad, bei dem die Höhe (in Fuß) durch den Ausdruck gegeben ist, wobei t die Zeit nach dem Start ist. Wann ist die Höhe des Balls am größten?

$$\color{BrickRed}h(t)=-25t^2+75t+24\\ \frac{dh}{dt}=-50t+75=0\\ \color{blue}t=1.5$$

$$h=-25\cdot 1.5^2+75\cdot1.5+24\\ \color{blue}h=80.25$$

The ball reaches its maximum height of 80.25 feet after 1.5 time units.

!

asinus Oct 21, 2019
edited by asinus  Oct 21, 2019